Hyperkahler manifolds and sheaves

Moduli spaces of hyperkahler manifolds or of sheaves on them are often non- separated. We will discuss results where this phenomenon reflects interesting geometric aspects, e.g. deformation equivalence of birational hyperkahler man- ifolds or cohomological properties of derived autoequivalences. In these con- siderations the Ricci-flat structure often plays a crucial role via the associated twistor space providing global deformations of manifolds and bundles.

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